The proportions of the "Dannebrog" are so because Danish flag law prescribes the relative widths of each block of color, including the fimbriations, and when you add all the pieces together you get those numbers.
John Ayer 5 February 1998

The dimensions of the square is usually given as one fifth by one quarter of
the height of the flag pole. However, the official decree on the flags of trade
ships from 1748 is that the white cross be 1/7 of the height of the flag, the
rear fields be square, and the two other fields be 6/4 of the length of the rear
fields. There was a tendency to make the flag longer, and in 1893 the ministry
of the interior stated that due to usage, no objections could be made as long as
the front fields where less than 7/4 of the rear ones.Peter Hans van den Muijzenberg, 20 June 2001

Scandinavian crosses are measured by the width of the color, as shown in the diagram above. In the case of Denmark, horizontally there are 12 units of red, 4 units of white, and 21 units of red. Vertically the flag has 12 units of red, 4 units of white and 12 units of red.

The two different red shades are approximated as Pantone 185c (for "land"
use) and 195c (for naval use). As far as I can see, the dark red is used only by
the flags used by the Navy - other maritime flags are of the "normal" red shade.
That would mean that there are in fact two variants of some flags.Zeljko Heimer, 10 June 2001

(Which more or less translates as:)
In spite of the lack of a flag law there are two red colours in the national
flag, to wit a darker red colour in the naval flag, called "orlogsrødt" (naval
red), which is only used on board of naval or state ships, and a lighter version
in the "splitflag" (swallow-tailed flag) and the square (rectangular) "stutflag"
(procession flag ), called "flagrødt" (flag red). The colors are also indicated
as "orlogsrødt" and "dannebrogsrødt" (Dannebrog red). Naval sites on land don't
use this naval red colour, which is only for use aboard ships.

For lack of a
flag law there apparently are no official pantone values, though I expect the
military will have defined some for its own use.

Danmarksbog
mentions that "It became customary for the State also to fly the swallow-tailed
flag ashore." This suggest that you shouldn't automatically assume a naval
context for the state flags. What's more, it shows only the Naval flag and the
Admiral's Standard as dark, whereas the National flag, the State flag, the Royal
standard, the Crown Prince's standard, the Regent's standard, the Chief of
Defence's standard, the DSB flag, the postal flag, the flag for State vessels,
and the revenue flag are all shown as light. Peter Hans van den Muijzenberg, 20 June 2001

In Danish, procession
flags are not really flags. We use 'flag' about cloth flown from flag poles or
masts, and 'fane' about procession flags or military (or other) colours. But
some of the cloth that we fly from flag poles are pennants, and they are not
really flags either. We use the term 'vimpel'. In some naval contexts, 'stander'
is used instead of 'vimpel'. A 'stander' is usually shorter than a 'vimpel'.
Now, some of our 'flag' (plural = singular) are swallow-tailed, 'splitflag'. If
they are rectangular instead, we use the term 'stutflag'.Ole Andersen, 24 June 2001

[The name of the Danish flag, Dannebrog, meaning 'banner of the Danes' or 'red
banner', occurs first in a Danish text 1478 and in a Dutch text 100 years
before; in the Dutch armorial Gelre (1370-86) a red banner with a red cross is
seen next to the arms of Valdemar 4. 'Atterdag'.]

Among the independent nations recognised by the UN, the Danish flag is
generally considered as the oldest continuously used national flag in the world. Regions, counts, kings and the like have had flags or banners older than Dannebrog, but no sovereign nation has used the same flag as long as Denmark.
Dennis Nielsen, 18 April 2001

Legend relates that the "Dannebrog" fell from the skies on 15 June 1219, the day in which King Waldemar II defeated the Estonians in battle.

The cross represents, unsurprisingly, Christianity.

Legend aside, there is a small controversy around the idea that the design was linked somehow to an ensign of the Holy Roman Empire. A white cross on a red background was used by the Empire in many of its provinces. A problem with this hypothesis exists in the fact that Denmark was never a province of the Holy Roman Empire. This question remains unresolved.

Danish State & War Flag/Ensign, from the FlaggenbuchEdward Mooney, Jr.
20 December 1999

A note to the figure of this flag in Album des Pavillonsexplains that the ships
without a Royal Standard may use this flag under masthead pennant (I guess
instead of the Royal Standard to indicate the presence of the King). The dark
red flag is shown, but I am sure that for -SW/--- usage the normal red is used.
Zeljko Heimer, 10 June 2001

On a visit to Denmark I saw state ships
flying a Splitflag with white crown. This makes them official Danish ships,
which means, as a crew member explained, that even though the ship he sailed on
was a small wooden ship, it still couldn't enter "Sweden" without asking
permission in advance. I also saw the Øvelses
kuttere Svane (Swane?) and Thyra, which flew a splitflag (I think) with a
crowned fouled anchor outlined in black. I was told that at one time the navy
had its own sports club which used this ensign, but that it no longer existed,
and now these two ships flew it. Peter Hans van den Muijzenberg, 27 August 2001

According to Pedersen
(1979), this ensign was proposed by the flag law commission of 1927.Ole Andersen, 24 April 2004

The customs flag with the words 'KONGELIGT TOLDFLAG' was introduced by the Customs Ordinance of 1 February 1797. It was replaced by a new customs flag by decision of the Queen dated 17. April 1987.

The new customs flag is the "Dannebrog" with swallow-tail as before but with a new emblem in white in the upper hoist red field (instead of the words). The emblem consists of crossed trident and caduceus surrounded by a wreath of laurel, all under a Royal crown.